Answer to Question #44340 in Linear Algebra for Aucun Désir

Question

Standard basis vectors for R^3 are (1,0,0),(0,1,0) and (0,0,1). If we want to insert u → into this basic, then which vector from standard basis can be removed while still maintaining the basis of R^3.
Discuss the case when:
u → =(4,3,6)
u → =(4,0,6)
Interpret the result geometrically in both cases.